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## Monday, April 29, 2013

### Multiple Choice Practice Questions on Atomic Physics and Quantum Effects for AP Physicsw B

“Being ignorant is not so much a shame as being unwilling to learn.”
– Benjamin Franklin

During March and April I have been unexpectedly busy and therefore could not post any thing here. Today I give you a few multiple choice practice questions on atomic physics and quantum effects along with their solution. This section will be interesting to most of you. Questions (with solution) in this section were posted on many occasions on this site. You may access them by clicking on the label ‘atomic physics and quantum effects’ below this post. Here are the additional questions:

(1) The energy of the electron in the hydrogen atom in the ground state is E1. When the hydrogen atom is in its first excited state, the energy of its electron is E2. Suppose we have a large number of hydrogen atoms in the ground state and radiation of frequency (E2 E1) is incident on these atoms. What happens?

(a) All atoms will jump to the first excited state.

(b) All atoms will continue to remain in the ground state.

(c) Some of the atoms will jump to the first excited state.

(d) Most of the atoms will jump to the second excited state.

(e) Most of the atoms will get ionised.

Since the energy of each photon in the incident radiation is equal to the energy difference between the ground state and the first excited state of the hydrogen atom, the probability of absorption of energy is high so that some of the hydrogen atoms will jump to the first excited state. The correct option is (c).

(2) The simple Bohr model is applicable to which one of the following?

(a) Atoms with light nuclei

(b) Atoms with heavy nuclei

(c) Helium atoms

(d) Doubly ionised lithium

(e) Uranium atoms

Doubly ionized lithium has just one electron moving around the nucleus and hence it is hydrogen-like. Therefore the simple Bohr model is applicable to it [Option (d)].

(3) A proton is moving through a region of space where a constant electric field acts along its direction of motion. The de Broglie wave length of the proton

(a) decreases with time

(b) increases with time

(c) remains constant

(d) varies in a sinusoidal manner

(e) goes on increasing first and soon becomes constant

The de Broglie wave length λ is given by

λ = h/p where h is Planck’s constant and and p is the momentum.

Since the proton is accelerated by the electric field, its momentum goes on increasing with time. Therefore, the de Broglie wave length λ of the proton decreases with time [Option (a)].

(4) An electron is projected at an acute angle with respect to a uniform magnetic field so that it travels along a helical path. The de Broglie wave length of the electron

(a) varies periodically

(b) increases with time

(c) remains constant

(d) decreases with time

(e) goes on decreasing first and attains a constant value

A static magnetic field cannot change the kinetic energy of a charged particle. The momentum of the electron therefore remains unchanged. Therefore the de Broglie wave length of the electron remains constant.